# Scaling policy iteration based reinforcement learning for unknown discrete-time linear systems

arXiv: https://arxiv.org/abs/2411.07825 · HTML: https://mlsanity.com/paper/2411.07825/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL theory and sample complexity, one of 15 directions in Deep reinforcement learning methods.
- Builds on 1 of its 30 references that are in the map.
- First posted on arXiv 12 Nov 2024.

## Placed in

- Deep reinforcement learning methods / [RL theory and sample complexity](https://mlsanity.com/deeprl/rl-theory-and-sample-complexity/)

## Builds on (most cited first, 1 of 1)

- [On The Convergence Of Policy Iteration-Based Reinforcement Learning With Monte Carlo Policy Evaluation](https://mlsanity.com/paper/2301.09709/) (2023)

## Built on by (most cited first, 1 of 1)

- [Stabilizer Design for Policy Iteration in Stochastic Linear Quadratic Control: A Spectrum-Assignment Approach](https://mlsanity.com/paper/2608.05953/) (2026)

## Abstract (arXiv)

In optimal control problem, policy iteration (PI) is a powerful reinforcement learning (RL) tool used for designing optimal controller for the linear systems. However, the need for an initial stabilizing control policy significantly limits its applicability. To address this constraint, this paper proposes a novel scaling technique, which progressively brings a sequence of stable scaled systems closer to the original system, enabling the acquisition of stable control gain. Based on the designed scaling update law, we develop model-based and model-free scaling policy iteration (SPI) algorithms for solving the optimal control problem for discrete-time linear systems, in both known and completely unknown system dynamics scenarios. Unlike existing works on PI based RL, the SPI algorithms do not necessitate an initial stabilizing gain to initialize the algorithms, they can achieve the optimal control under any initial control gain. Finally, the numerical results validate the theoretical findings and confirm the effectiveness of the algorithms.